what is the definition of "acoustic center" ?
@herbreichert The point in space from which sound appears to originate in terms of time. Think of a woofer and tweeter mounted on a flat baffle. Look at it from the side. The tweeter's acoustic center is practically at the baffle, but the woofer's may be 1" or more behind the baffle. Speaker designers have to take this into consideration for either phase or time alignment.
how do we know when they are aligned? A tone burst?
Kind of depends how you mean "alignment." Phase aligned you can tell by an smooth transition from one driver to the other. Time aligned you can see using a step response. See figure 9 in these measurements for time aligned speaker step response.
what is the definition of a point source?
A theoretical "ideal" (one of many ideals) in which the full range of sound appears to come from a single point in space. A single, full-range driver is by definition a point source. Some multi-way speakers may attempt to mimic this behavior in time and space. The Duntech Sovereign is a famous, early-ish example.
Contrast to a line-source, like the famous Infinity RS.